If p₁ and p² are mutually perpendicular principal stresses acting on a soil mass, the normal stress on any plane inclined at angle ?? to the principal plane carrying the principal stress p₁, is: A) (p₁ ? p²)/2+ (p₁ + p²)/2 sin 2? B) (p₁ ? p²)/2+ (p₁ + p²)/2 cos 2? C) (p₁ + p²)/2+ (p₁ ? p²)/2 cos 2? D) (p₁ + p²)/2+ (p₁ ? p²)/2 sin 2?

Question

Quizplus · Accepted Answer

The normal stress on any plane inclined at an angle to the principal plane can be found using the formula $\sigma_n = \frac{\sigma_1 + \sigma_2}{2} + \frac{\sigma_1 - \sigma_2}{2} \cos 2\theta$, where $\sigma_1$ and $\sigma_2$ are the principal stresses and $\theta$ is the angle of inclination. This matches option C.

If P1 and P2 Are Mutually Perpendicular Principal Stresses Acting

If P₁ and P² Are Mutually Perpendicular Principal Stresses Acting